So don't use Rio primers or spend time and figure out your problem. If your firing pin strikes are less on the right side than the left it will cause this problem. If your rim cut is slightly deeper it will do the same. But unless you just have to use Rio primers I would just use other brands and not worry about it very much.

When they went off in the left barrel that should have told you the problem was in your gun not the primers. You never had a left side failure to fire just right side. so your problem is right side only. If you moved the "bad" shell to the left side it was instantly good. If you measure your firing pin striking depth the right side is most likely less than the left. The right side does get more use. If it bother you that much you can get it corrected but just changing brands of shells will correct it as well.